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one at either end, by means of which the bubble can be brought to the center of its run, as in the case of the Y level, when the line of collimation is brought to the proper level by Mr. Gravatt's method of adjustment, already explained.

The telescope is attached to a horizontal bar, in a similar manner to Troughton's level, but room is just left between the telescope and the bar for the compass-box.

A cross level, k, is placed upon the telescope at right angles to the principal level 7 l, by which we are enabled to set the instrument up at once with the axis nearly vertical. A mirror, m, mounted upon a hinge-joint, is placed at the end of the level ll, so that the observer, while reading the staff, can at the same time see that the instrument retains its proper position -a precaution by no means unnecessary in windy weather, or on bad springy ground.

The telescope is attached to the horizontal bar by capstanheaded screws, B B, as in Troughton's level, by which the line of collimation is set perpendicular to the vertical axis; and the instrument is set up upon parallel plates, as before described, for the Y level.

The operation of determining the difference of level between two stations by observations made at a single station is called simple levelling, and is performed as follows:

K

Let A and H be two points whose difference of level is required. Plant the instrument at D, and adjust it to a horizontal position. Read off A c, the height of a staff held at A, then turn the telescope round and read off E H, the height of a similar staff, or of the same staff held at H. Then A c is the height of K, the axis of the telescope above the point a, and EH is the height of K above another point, H; and it is clear that EH-AC=GH, the difference of level between a and H.

In this operation the station A, at which the staff is first read off, is called the back station, and the station H is called the fore station; and, if the reading of the staff at the back station be greater than that at the fore station, the difference of level is called a rise; but, if the reading at the back station be less

than that at the fore, as in the example just given, the difference of level is called a fall.

When, from the nature of the ground, or the great distance between the two points, they cannot both be observed from a single spot, a series of simple levels must be taken, the fore station at each operation being made the back station at the next operation; and from the combination of all the results thus obtained the required difference of level is obtained. In these operations care must be taken, in going over soft ground, lest the staff at the fore station, when turned round to be read as the staff at the back station in the next operation, should sink further into ground; and, to prevent this, the foot of the staff must be placed upon a flat, hard substance, as a piece of slate or tile. There is a simple instrument called a tripod, sold for this purpose by the instrument makers, being simply a plate of iron with a small rounded projection in the center, two small spikes at the side to fix it in its place, and a short chain to lift it by, when the staff-holder wishes to remove from his place.

In determining by this method the difference of level be.tween two distant points, it is immaterial by what route we proceed from one to another, so that such spots may be selected for the intermediate stations as are most convenient for the purpose. The bearings of the stations from the instrument are also matter of indifference; but, the more nearly the instrument is equidistant from the two stations observed at each operation, the more correct will be the result obtained, the errors in the back readings compensating, for the most part, the errors in the fore readings, whether the errors arise from refraction and curvature†, or from the imperfect adjustment of the instrument.

If, then, the object be only to obtain the difference of level of two points, we have only to record in two separate columns the readings of the staff at the back stations and fore stations respectively, and the difference of the sums of these readings

* The error of refraction is that arising from the bending of the rays of light during their passage through the atmosphere, and makes all objects appear higher than they really are.

The object of levelling is to determine points upon a spherical surface or equally distant from the earth's center, or to determine the differences of the distances of a series of points from the earth's centre. The line of sight, or prolongation of the line of collimation, however, is a tangent to the spherical surface, and therefore the points observed upon this line are really above the level of the point of observation. The correction for curvature is therefore additive, while that for refraction is subtractive.

will be the difference of level required. Thus, if the difference of level between two points A and B, be required, and if the readings at A and B, and three intermediate stations

O 2,

3, be recorded as follows, viz.:

Back O

Fore

1,

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Then 22-18 feet is the fall from A to в, or A is 22.18 feet above B. When, however, it is required not only to find the difference of level between two distant points, but to make such observations as shall enable us to draw a section exhibiting the undulations of the ground along some specified route from the one point to the other, then the stations must be so chosen that one of them shall be at the commencement of each change in the inclination of the ground; the distances between the sta tions must also be carefully measured; and it is further advis able to note the distances and bearings of the stations from the instrument, which it will be more convenient now to place on a point in the specified route between the stations.

In drawing the section, it is the horizontal distances between the several stations that must be laid down. For short distances, or over very irregular ground, such horizontal measurements may be obtained by bidding an assistant hold one end of a measuring tape close to the ground at the highest end of the distance, and holding the other end above the ground, stretching the tape in a horizontal line, a stone let fall from this end then marking upon the ground the point to which the measurement reaches. But, when the ground rises and falls in long regular slopes, the measurements should be taken along the slopes, and then be reduced to horizontal distances by calculation. If the rise or fall is but slight, this reduction may be altogether disregarded, the difference between the horizontal and hypothenusal measurements not exceeding the limits of error in the measure itself.

Care should be taken to record all the observations in a clear and intelligible form, and for this purpose a field book may be prepared of the following form:

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In the first column are entered the distances between the several stations, which, being successively added to the preceding total, give the total distances of each station from the starting point: in the next column are entered the distances of the stations from the instrument; and in the third are

entered the bearings of the stations from the instrument. In the fourth and fifth columns are entered the readings of the staves; and in the sixth column the heights above datum of the several stations are computed by adding the back reading to the height last found, and subtracting the fore reading from the sum. The seventh and eighth columns are added for per forming the reduction of the measured distances to horizontal distances, when the slope is sufficient to render this reduction necessary. In carrying forward the distances to the next page of the book, the total reduced horizontal distance should be carried to the top of the first and second columns instead of the total measured distance along the slope; but such sub stitutions should not be made at any other part of the page, as it would interfere with the proof of the distances by adding up the second column, which ought to produce the last dis tance entered in the first. The levels are proved by subtract ing the sum of the numbers in the sixth column from the sum of the numbers in the fifth, when the remainder should be the height above datum of the last station recorded at the bottom of the page.

To facilitate the reduction of the measured distances to the corresponding horizontal distances, the following table showing the reduction upon each 100 feet for each foot difference of level should be inserted in the field book:

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Difference of Reduction Level for 100 upon 100 feet feet distance. of distance.

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When it is required to plot the section on a large scale, and to show every undulation of the surface, it is not necessary to remove and re-set the instrument to obtain the height, above datum of every point necessary to be known for this purpose; but, besides reading the staff at the back and fore station, it may be read off from the same place of the instrument, at as many intermediate points as may be deemed

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